The stratified approximation assumes that the surface which receives the radiations is flat and the source is far. Thus only one space variable is retained. For such cases, an integral formulation, probably due to Chandrasekhar [1]}, turns out to be much more precise and also computationally much cheaper. A fixed-point iteration scheme on this nonlinear integral formulation, known in the radiative transfer community as “iterations on the
sources" was shown to be monotone in [2]}, a property which seems to have escaped earlier studies. Finally in [3]},and [4]} the method was extended to include the temperature equation of the fluid and also to handle Rayleigh scattering while retaining
monotonicity.
In [5]} F. Golse observed that the integral formulation exists also in 3D. A new existence result was proved by using this formulation and it was numerically tested. However the computing cost was \(O(N^2)\) , \(N\)  being the number of vertices of the triangulation of the physical domain.
